Source: Cyberchase: “Double Trouble”
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In this video segment from Cyberchase, Harry plays a game of chess with a young friend and suggests a wager on the game. Harry’s friend uses a story to explain how putting a penny on the first square and then doubling the amount on each square of the chessboard can generate a tremendous amount of money over time.
Download and ShareHere are some Frame, Focus and Follow-up suggestions for using this video in a math lesson.
What is Frame, Focus and Follow-up?
Frame: How do you double an amount? For example if you have five pennies, how much would you have if you doubled that amount? How about if you doubled it again? What do you think would happen if you kept doubling that amount, say four or five times? How about twenty times? What mathematical operation are you using?
Focus: As you watch the video segment, think about how the penny amounts increase on the chessboard as the doubling occurs. Which wager would pay out more money, the five dollar wager or the doubling pennies?
Follow Up: Which wager amount was more? The five dollar wager or the doubling pennies? When we double an amount, what are we multiplying it by? After doubling a small amount, only nine or ten times, we can see that it increases dramatically. Why does that happen?
HARRY: I'm gonna beat you.
BOY: I don't think so.
HARRY: How much you wanna bet?
BOY: Don't you know gambling is wrong?
HARRY: I'll bet you five dollars I can beat you.
BOY: Let's pretend we're going to make a bet, which we're not, because then my mom would never let you baby-sit for me ever again. If you were really sure you were going to win, which would you bet: five dollars or a bunch of pennies?
HARRY: How big a bunch?
BOY: One penny on this square, two pennies on the next, four here, eight here. Keep doubling the number of pennies from square to square for the whole board.
HARRY: Pennies or dollars? Of course, I'd bet five dollars.
BOY: Well, let me tell you a story that may change your mind. It's the legend of the grain of rice.
BOY: Once upon a time there was a rotten king.
HARRY AS THE KING: What do you want, you miserable peasant?
Boy as the peasant: Even though you are a selfish tyrant who keeps all the kingdom's riches for yourself while the people have nothing to eat, I made this chessboard for you, your majesty.
HARRY AS THE KING: Now I suppose you'll want a reward.
Boy as the peasant: No, that's not necessary.
HARRY AS THE KING: If I say you're getting a reward, you're getting a reward.
Boy as the peasant: Whatever you wish.
HARRY AS THE KING: Okay. So what'll it be? My autograph? A picture of me?
Boy as the peasant: Simply give me some rice so that my family can eat. Put one grain of rice on the first square of your chessboard. Two grains on the second.
HARRY AS THE KING: Oh! You mean double the number of grains from square to square?
Boy as the peasant: Right, on every square.
HARRY AS THE KING: A few grains of rice? I shouldn't take advantage of such foolishness, but I can't help myself. Okay, it's a deal.
BOY: So, on the first square, the king put one grain of rice. On the second, he put two.
HARRY AS THE KING: Two times one equals two. What a fine feast this makes for a fool!
BOY: The king then put four, eight, sixteen...
HARRY: Then 2x16, that's 32...
BOY: And so on and so on. By the time the king got to the 16th square, the number of grains was 32,768 which weighs about one pound. The grains and pounds continued to double, soon burying the king in rice.
HARRY AS THE KING: There won't be any rice left for me!
BOY: Pounds of rice soon became tons. Then the tons doubled, too. By the time the king gave the peasant rice for all 64 squares on the chessboard, the total was more than 500 billion tons of rice! That's enough to cover the surface of the earth twice!!
HARRY AS THE KING: I've given away all my rice!
Boy as the peasant: Now I can feed my family and all the other hungry people in the world. Thanks, your majesty.
HARRY: So, the fool was the king.
BOY: Right. So, if we were to make a bet -- which we're not -- would you wager the five dollars or the bunch of pennies?
HARRY: Five dollars.
BOY: Didn't you get the point of the story?
HARRY: Of course I did. The bunch of pennies would be worth billions of dollars.
BOY: And?
HARRY: You beat me.
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